On the relationship between interval observers and invariant sets in fault detection

In this paper, the relationship between two settheoretic fault detection (FD) approaches, the interval observerbased and the invariant set-based approaches, is investigated. In FD, interval observers monitor the system dynamic behavior in real time and generates adaptive intervals for system outputs. Invariant sets focus more on steady state behavior of the system rather than the transient behavior. This paper discusses these two approaches, presents the relationship between them and compares them in the FD task. At the end, a numerical example is used to illustrate the relation between these two approaches